Complex manifolds with split tangent bundle

Details Complex manifolds with split tangent bundle Complex manifolds with split tangent bundle

1998-09-07

arxiv.org/abs/math/9809033v2

Mathematics

Algebraic Geometry

9 pages, Plain TeX. We give a simpler proof of Theorem A following a paper of Yau

Scientific paper

Let X be a compact Kaehler manifold. We expect that any direct sum decomposition of the tangent bundle T(X) comes from a splitting of the universal covering space of X as a product of manifolds, in such a way that the given decomposition of T(X) lifts to the canonical decomposition of the tangent bundle of a product. We prove this assertion when X is a Kaehler-Einstein manifold or a Kaehler surface. Simple examples show that the Kaehler hypothesis is necessary.

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